The slides to my presentation of the paper on January 7th, 2013 in New Orleans, LA, USA is available: alenex13esais-slides.pdf . They contain little text and an example of the eSAIS algorithm with a simplified PQ.

We have also submitted a full version of the eSAIS paper to a journal. Due to long publication cycles, we make a pre-print of the journal article is available here: esais-preprint.pdf . The full paper contains more details on the inducing algorithm for the LCP array and additional experimental details.

This semester I had the pleasure to take part in a lab exercise course supervised by Prof. Thomas Linß at the FernUniversity of Hagen. The objective was to comprehend, implement and evaluate a particular recent advancement in the field of numerical mathematics. My topic was finding the roots of a polynomial by clipping in Bézier representation using two new methods, one devised by Michael Bartoň and Bert Jüttler [1], the other extended from the first by Ligang Liu, Lei Zhang, Binbin Lin and Guojin Wang [2].

My implementation of this topic was done for the lab course in C++ and contains many in themselves interesting sub-algorithms, which are combined into the clipping algorithms for finding roots. These sub-algorithms may prove useful for other purposes, which is the main reason for publishing this website. Among these are:

Algorithms to convert from monomial to Bézier representation and vice versa: PolynomialStandard::toBezier() and PolynomialBezier::toStandard().

Evaluation algorithms for both representations: Horner's Schema and the Algorithm of de Casteljau.

Another version of de Casteljau's Algorithm to split a polynomial in Bézier representation into two parts.

Jarvis' March aka gift wrapping (run time O(hn)) to calculate the convex hull of the Bézier polygon: PolynomialBezier::getConvexHull().

Cardano's formulas to find all real roots of any cubic polynomial: PolynomialStandard::findRoots().

For the lab course I wrote two documents, both in German: one is an abstract Kurzfassung.pdf (1 page), which is translated into English below, and the other a short report Ausarbeitung.pdf (6 pages). The report contains a short description of the algorithms together with execution and convergence speed measurements, which verify the original authors experiments. For presenting the lab work I created these Slides.pdf , which however are not self-explanatory due to my minimum-text presentation style.